Simple implementation of a Physics-Informed Neural Networks in Pytorch for inverse problems

 https://colab.research.google.com/drive/1ycheGcblVg38FK662NzShspXudTE3ugg?usp=sharing

class Net_IP(nn.Module):

def __init__(self):

super(Net_IP, self).__init__()

self.input_layer_u = nn.Linear(2,100)

self.hidden_layer1 = nn.Linear(100,10)

self.output_layer_u = nn.Linear(10,1)

self.input_layer_mu = nn.Linear(1,10)

self.hidden_layer2 = nn.Linear(10,3)

self.output_layer_mu = nn.Linear(3,1)

def forward(self, x, t):

# temperature field

inputs_u = torch.cat([x,t],axis=1) # spatio-temporal coordinate

layer1_out = torch.sigmoid(self.input_layer_u(inputs_u))

layer2_out = torch.sigmoid(self.hidden_layer1(layer1_out))

output_u = self.output_layer_u(layer2_out)

# diffusion field

inputs_mu = x # spatial coordinate

layer3_out = torch.sigmoid(self.input_layer_mu(inputs_mu))

layer4_out = torch.sigmoid(self.hidden_layer2(layer3_out))

output_mu = torch.nn.functional.softplus(self.output_layer_mu(layer4_out))

# concatenation

output = torch.cat([output_u,output_mu],axis=1)

return output

net_IP = Net_IP()

net_IP = net_IP.to(device)